So she visited a doctor who gave her a blood test that’s often used to check a woman’s egg supply. It works by looking for anti-Müllerian hormone, or AMH, which is secreted by growing follicles, the sacs that house each egg.

The results were not good, she was told. Her AMH was too low and her follicle stimulating hormone level was too high, both indicators of diminished egg quantity. In other words, it would most likely take multiple procedures to bank enough eggs.

At about $15,000 each, the cost was prohibitive, and her insurance didn’t cover egg freezing or fertility treatments. A nurse suggested that she use donor eggs.

“I was pretty devastated,” Ms. Bourquin said.

Two years later, she remarried. Ms. Bourquin and her husband conceived naturally on the first try. Her doctor was “stunned,” Ms. Bourquin said.

“We even went and bought a lottery ticket,” she said. “We were like, are you kidding me?”

New research published last week in the Journal of the American Medical Association underscores what Ms. Bourquin experienced, and what many fertility experts have already observed: AMH doesn’t dictate a woman’s reproductive potential. And although AMH testing is one of the most common ways that doctors assess a woman’s fertility — it’s especially important for women struggling with infertility — an AMH value isn’t always telling.

Dr. Zev Rosenwaks, director of the Center for Reproductive Medicine at Weill Cornell Medicine and NewYork-Presbyterian, called the study “elegant.”

“All it takes is one egg each cycle,” he said. “AMH is not a marker of whether you can or cannot become pregnant.”

Age is more than just a number

For women who haven’t yet tried to get pregnant and who are wondering whether they are fertile, an AMH value “isn’t going to be helpful in that context,” said Dr. Esther Eisenberg, the program director of the Reproductive Medicine and Infertility Program at the National Institutes of Health, which helped fund the study. In addition, “AMH wouldn’t necessarily be a good marker to tell you when you ought to freeze your eggs.”

Doctors don’t yet have a way to definitively predict egg quality or a woman’s long-term ability to conceive, but age is one of the most important factors.

“I really do feel like that’s all we have right now,” said Dr. Anne Z. Steiner, the lead researcher of the study and a professor of reproductive endocrinology and infertility at the University of North Carolina in Chapel Hill.

Her study followed 750 women between the ages of 30 and 44 who had been trying to conceive for three months or less. During the 12-month observation period, those with low AMH values of less than 0.7 were not less likely to conceive than those who had normal AMH values.

The study has various limitations, however, that are worth noting. The researchers only included women who did not have a history of infertility. Women who sought fertility treatments (about 6 percent) were withdrawn. And only 12 percent of the women were in the 38-to-44 age range. In addition, the number of live births was unavailable. Dr. Steiner says she’ll next look at whether low AMH is associated with a higher risk of miscarriage among the women who conceived.

Ms. Bourquin’s daughter is now 2 years old, and she is hoping for a second child. But at 41, things aren’t as easy this time around.

For months she and her husband tried unsuccessfully to conceive naturally. After three failed attempts at intrauterine insemination, or IUI, and a failed egg retrieval, they are trying IUI yet again.

One of Dr. Steiner’s earlier studies, published in June of last year, shows that women experience a significant reduction in fertility in their late 30s.

“There’s no one age where a woman turns into a pumpkin,” Dr. Steiner said, but there are slight declines in fertility after the age of 35, followed by steeper drop-offs.

“The difference between 30 and 33 is negligible,” she said. “But the difference between 37 and 40 is going to be pretty drastic.”

Searching for a ‘golden egg’

Although AMH testing isn’t designed to be an overall gauge of a woman’s fertility, it can still provide valuable information, especially for “women who are infertile and seeking treatment,” Dr. Rosenwaks said.

It can assist in diagnosing polycystic ovarian syndrome, and identify when a woman is getting close to menopause.

Previous research also shows that AMH is pretty good at predicting a woman’s response to ovarian stimulation for in vitro fertilization, Dr. Steiner said, and it can predict the probability of conceiving via I.V.F.

That was the case for Lauren Donato, 37, who has spent about $50,000 trying to conceive, mainly via I.V.F., after learning last year that her AMH was very low. She recently moved back in with her parents to avoid going into debt.

She thought about freezing her eggs a decade ago. At the time, she said, she was told not to worry about her fertility.

“My O.B. kept saying, ‘You’re so young,’” Ms. Donato said. “I kept saying, there has to be some sort of test.”

As the years passed, Ms. Donato, a mental health counselor from Brooklyn, who is single, continued to think about having children.

Last year, when she was 36, one of her doctors finally tested her AMH.

Anything under 1 is typically considered a low AMH value for a woman her age, she was told. Hers was 0.1.

She visited a reproductive endocrinologist who suggested that she try I.V.F. now.

“The doctor pretty much said, ‘You’re going to have a baby now or you’re not going to have any kids,’” Ms. Donato recalled.

She selected a sperm donor and has been trying to find her “golden egg” — that one egg that will result in a pregnancy — ever since. Egg quality declines as women age, so it’s a more difficult proposition than it might have been 10 years ago. “Quantity means nothing, it’s quality,” she said. “And there’s no test for quality.”